Answer
number to be added: $\dfrac{1}{16}$
factored form: $(x-\frac{1}{4})^2$
Work Step by Step
RECALL:
To complete the square of an expression in the form $x^2-bx$, $(\frac{b}{a})^2$ must be added.
The factored form of the result is $(x-\frac{b}{2})^2$.
Thus, in the given expression add $(\dfrac{\frac{1}{2}}{2})^2=(\frac{1}{4})^2=\frac{1}{16}$ to obtain:
$x^2 -\frac{1}{2}x + \frac{1}{16}$
Writing the square in factored form gives:
$x^2-\frac{1}{4}x+\frac{1}{16} = (x-\frac{1}{4})^2$
